Topic
Renewal theory
About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.
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TL;DR: In this article, a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities is presented. But the authors do not consider whether the sample distribution is regenerative or non-regenerative.
Abstract: This thesis consists of four papers.In paper 1, we prove central limit theorems for Markov chains under (local) contraction conditions. As a corollary we obtain a central limit theorem for Markov chains associated with iterated function systems with contractive maps and place-dependent Dini-continuous probabilities.In paper 2, properties of inverse subordinators are investigated, in particular similarities with renewal processes. The main tool is a theorem on processes that are both renewal and Cox processes.In paper 3, distributional properties of supercritical and especially immortal branching processes are derived. The marginal distributions of immortal branching processes are found to be compound geometric.In paper 4, a description of a dynamic population model is presented, such that samples from the population have genealogies as given by a Lambda-coalescent with mutations. Depending on whether the sample is grouped according to litters or families, the sampling distribution is either regenerative or non-regenerative.
40 citations
TL;DR: In this paper, the authors discuss the advantages and disadvantages of available solution techniques for random pulse problems in non-linear stochastic dynamics, both those which do and do not lead to Markov theory.
40 citations
TL;DR: In this paper, a population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process.
Abstract: A population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process. Each particle alive at the time of a disaster, survives it with probability p and the survival of any particle is assumed independent of the survival of any other particle. The asymptotic behavior of the mean of the process is determined and as a consequence, necessary and sufficient conditions are given for extinction.
40 citations
TL;DR: A bimodal distribution, with two peaks, consisting of a weighted sum of two normal probability distributions to describe different vehicle loads is developed according to acquired traffic load data.
40 citations
TL;DR: In this article, a simple approach based on Renewal Theory is proposed to determine the precise asymptotic behavior of the partition function, from which the scaling limits of the models and an explicit construction of the infinite volume measure in all regimes, including the critical one are obtained.
Abstract: We consider continuous and discrete (1+1)-dimensional wetting models which undergo a localization/delocalization phase transition. Using a simple approach based on Renewal Theory we determine the precise asymptotic behavior of the partition function, from which we obtain the scaling limits of the models and an explicit construction of the infinite volume measure in all regimes, including the critical one.
40 citations